At the Nyquist frequency, and for , such filter gains
and we have to use
to have the correct attenuation at high frequency. Fig. 5
shows the magnitude and phase delay (in seconds) obtained with the
first-order filter for three values of its parameter .

By comparison of the curves of Fig. 4 with the
responses of Fig. 5, we see how the latter can be used to
represent the losses in a section of one-dimensional waveguide
section. Therefore, the simulation scheme turns out to be that of
Fig. 6. Of course, better approximations of the curves of
Fig. 4 can be obtained by increasing the filter order
or, at least, by controlling the zero position of a first-order
filter. However, the form (50) is particularly attractive
because its low-frequency behavior is controlled by the single
parameter .

Figure 5:
Magnitude and phase delay of a first-order IIR filter, for different values of the coefficient , is set to
with the same values of used for the curves in fig. 4